Answer:
Step-by-step explanation:
A. y-Intercept of ƒ(x)
ƒ(x) = x² - 4x + 3
f(0) = 0² - 4(0) + 3 = 0 – 0 + 3 = 3
The y-intercept of ƒ(x) is (0, 3).
If g(x) opens downwards and has a maximum at y = 3, it's y-intercept is less than (0, 3).
Statement A is TRUE.
B. y-Intercept of g(x)
Statement B is FALSE.
C. Minimum of ƒ(x)
ƒ(x) = x² - 4x + 3
a = 1; b = -4; c = 3
The vertex form of a parabola is
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
h = -b/(2a) and k = f(h)
h = -b/2a = -(-4)/(2×1 = 2
k = f(2) = 2² - 4×2 + 3 =4 – 8 +3 = -1
The minimum of ƒ(x) is -1. The minimum of ƒ(x) is at (2, -1).
Statement C is FALSE.
D. Minimum of g(x)
g(x) is a downward-opening parabola. It has no minimum.
Statement D is FALSE
Answer: y=-.667x+1
Step-by-step explanation:
1. Firstly, substitute the coordinates of the two points into the slope intercept equation:
(1) y₁ = mx₁ + b
(2) y₂ = mx₂ + b
2. Then, subtract the first equation from the second:
y₂ - y₁ = m(x₂ - x₁)
3. Finally, divide both sides of the equation by (x₂ - x₁) to find the slope:
m = (y₂ - y₁)/(x₂ - x₁)
4. Once you have found the slope, you can substitute it into the first or second equation to find the y-intercept:
y₁ = x₁(y₂ - y₁)/(x₂ - x₁) + b
b = y₁ - x₁(y₂ - y₁)/(x₂ - x₁)
Let width = w
length = 4w/3
Area = 432 = length*width = w*4w/3
4w^2/3 = 432
w^2 = 432*3/4 = 324
w = 18
so the width of the cake pan is 18 inches.